Question 1165088
assuming you are given {{{f(x)=4sqrt(x^2-8x)}}} and {{{g(x)= 5sqrt(5x^2-14x)}}}


to find the domain of 

{{{f(x)=4sqrt(x^2-8x)}}}

look for restrictions: Check for values that make the function undefined (e.g., division by zero).

will be if

{{{x^2-8x=0) }}}=>  {{{x^2=8x}}}=>{{{x=8}}} or {{{x=0}}}

Consider square roots: Ensure the expression under any square root is non-negative.

{{{sqrt(x^2-8x)>0}}}
{{{x^2-8x>0}}}
{{{x^2>8x}}}
{{{x>8}}}

so, the domain is:

({{{-infinity}}}, {{{0}}}] U [{{{8}}}, {{{infinity}}})

or

{ {{{x}}} element of {{{R}}}| {{{x<=0}}}, {{{x>=8}}}  }



{{{g(x)= 5sqrt(5x^2-14x)}}}...........find it same way as above

({{{-infinity}}}, {{{0}}}] U [{{{14/5}}},{{{ infinity}}})

{ {{{x}}} element {{{R}}} : {{{x<=0}}} or {{{x>=14/5}}} }